Derivative of ln (x) using the definition of derivative
I used the definition of the derivative to show that d/dx ln(x) =1/x
Жүктеу.....
Пікірлер: 36
@WolfgangFeist6 ай бұрын
Second last step: you need to use "continuity" of ln(x). (Because:with still finite x/h the term in the ln is not yet 'e'). BTW: I love the way you are presenting this explaining every step (in a calm and friendly way). Most teachers try to do it in a hurry. That is the main reason, why some students get annoyed with math.
@SpiroGirah3 жыл бұрын
I never thought of this! Good job!
@temporarychannel975911 ай бұрын
the enthusiasm made this really enjoyable to watch, great job
@averagestudent52227 ай бұрын
This guy turns math into magic
@barthennin6088 Жыл бұрын
Beautiful! 1st time seeing this truly from first principles!
@ecSruthipriyaMahesh2 ай бұрын
I really like your classes, thank you for your hard work! 😃
@boguslawszostak17842 ай бұрын
If you define ln(x) as the integral from 1 to x of 1/u du, you have no problems computing its derivative. It is equal to 1/x by definition of the function.
@manoharkanade7383 Жыл бұрын
Very good explanation ❤
@nellwackwitz2 жыл бұрын
You are AWESOME!!
@Th3OneWhoWaits4 ай бұрын
8:58 as h goes to 0, "n" or x/h goes to infinity. Thus, lim as h goes to 0 = lim n goes to infinity.
@licksorestockpile119011 ай бұрын
Solid videos!
@surendrakverma5553 ай бұрын
Very good. Thanks 👍
@sldw3221 Жыл бұрын
Hello sir, i'm seeing that we always using definition of e with limit while proving all of these formulas but is it actually possible for you to explain or prove how or why limit n->infinity (1+1/n)^n is equal to euler's number? Did you record a video about this or would you talk about that in another video if it's possible? Thanks
@Harrykesh630Ай бұрын
just a suggestion 😁 It might be too late to point out but, you could have started by first proving that ln(x) is indeed differentiable by Left and Right hand derivative then go on to find it.
@nichodimuszishiritinashe83292 жыл бұрын
You are the best
@alexdcruz36823 ай бұрын
Love your videos
@user-bi1ky8se8q6 ай бұрын
You are a great man
@user-ov2lc8xo5x2 ай бұрын
Great job
@wira25625 ай бұрын
It's very useful to understand the inderivatived integral of dx/x sir!
@robertveith6383
15 сағат бұрын
Use grouping symbols: (dx)/x
@wilsonhicke559821 күн бұрын
Love this
@hassanejturay299410 ай бұрын
Awesome
@salamalmudarris5032 Жыл бұрын
But n is integer while x/h is real number?
@elai31472 жыл бұрын
5:31, as h goes to zero wouldn't x/h go to either positive infinity or negative infinity?
@xavierwainwright8799
Жыл бұрын
This works because lim x-> -inf (1+1/x)^x is also equal to e, but I don't know any proofs without using the derivative of ln(x) (this would be circular reasoning).
@tigergold5990
Жыл бұрын
@@xavierwainwright8799 take lim x-> -inf (1 + 1/x)^x substitute w = -x, so as x -> inf w -> inf = lim w -> inf (1 - 1/w)^(-w) = lim w -> inf e^ ln((1 - 1/w)^(-w)) bring -w out front with log rules = lim w -> inf e^( -w * ln(1 - 1/w) ) rewrite the subtraction inside the natural log = lim w -> inf e^( -w * ln((w - 1)/w) ) rewrite division inside ln as subtraction of lns = lim w -> inf e^( -w * ( ln(w - 1) - ln(w) ) ) use the negative sign on w in the exponent to switch the order of subtraction = lim w -> inf e^( w * ( ln(w) - ln(w - 1) ) ) recombine logs and bring the w inside as an exponent = lim w -> inf e^ln( (w / (w - 1)) ^ w ) cancel the exponential and log = lim w -> inf (w / (w - 1))^w substitute w = n + 1, so as w -> inf n also -> inf = lim n -> inf ((n + 1)/n))^(n + 1) take out the base of the n+1 exponent to get rid of the 1 = lim n-> inf ((n+1)/n)^n * (n+1)/n write limit of product as product of limits = lim n-> inf ((n + 1)/n)^n * lim n-> inf (n + 1)/n first limit is the normal form of the limit for e, second limit is easily calculated to be 1 = e
@cblpu5575
Жыл бұрын
Recall that the domain of ln (x) is **positive real numbers only** hence x/h is a positive real number x divided by a quantity h tending to zero
@sandraboateng5435 Жыл бұрын
😍😍👌👌✊✊👍👍
@katiatzo8 ай бұрын
BRAVO
@januszek17605 ай бұрын
(1 + 1/(x/h))^(x/h) is not equal e
@samwelkariuki3114 Жыл бұрын
Always the best teacher.....what about 1/x
@PrimeNewtons
Жыл бұрын
Thanks
@holyshit922 Жыл бұрын
He missed step when he used fact that ln is continuous
Пікірлер: 36
Second last step: you need to use "continuity" of ln(x). (Because:with still finite x/h the term in the ln is not yet 'e'). BTW: I love the way you are presenting this explaining every step (in a calm and friendly way). Most teachers try to do it in a hurry. That is the main reason, why some students get annoyed with math.
I never thought of this! Good job!
the enthusiasm made this really enjoyable to watch, great job
This guy turns math into magic
Beautiful! 1st time seeing this truly from first principles!
I really like your classes, thank you for your hard work! 😃
If you define ln(x) as the integral from 1 to x of 1/u du, you have no problems computing its derivative. It is equal to 1/x by definition of the function.
Very good explanation ❤
You are AWESOME!!
8:58 as h goes to 0, "n" or x/h goes to infinity. Thus, lim as h goes to 0 = lim n goes to infinity.
Solid videos!
Very good. Thanks 👍
Hello sir, i'm seeing that we always using definition of e with limit while proving all of these formulas but is it actually possible for you to explain or prove how or why limit n->infinity (1+1/n)^n is equal to euler's number? Did you record a video about this or would you talk about that in another video if it's possible? Thanks
just a suggestion 😁 It might be too late to point out but, you could have started by first proving that ln(x) is indeed differentiable by Left and Right hand derivative then go on to find it.
You are the best
Love your videos
You are a great man
Great job
It's very useful to understand the inderivatived integral of dx/x sir!
@robertveith6383
15 сағат бұрын
Use grouping symbols: (dx)/x
Love this
Awesome
But n is integer while x/h is real number?
5:31, as h goes to zero wouldn't x/h go to either positive infinity or negative infinity?
@xavierwainwright8799
Жыл бұрын
This works because lim x-> -inf (1+1/x)^x is also equal to e, but I don't know any proofs without using the derivative of ln(x) (this would be circular reasoning).
@tigergold5990
Жыл бұрын
@@xavierwainwright8799 take lim x-> -inf (1 + 1/x)^x substitute w = -x, so as x -> inf w -> inf = lim w -> inf (1 - 1/w)^(-w) = lim w -> inf e^ ln((1 - 1/w)^(-w)) bring -w out front with log rules = lim w -> inf e^( -w * ln(1 - 1/w) ) rewrite the subtraction inside the natural log = lim w -> inf e^( -w * ln((w - 1)/w) ) rewrite division inside ln as subtraction of lns = lim w -> inf e^( -w * ( ln(w - 1) - ln(w) ) ) use the negative sign on w in the exponent to switch the order of subtraction = lim w -> inf e^( w * ( ln(w) - ln(w - 1) ) ) recombine logs and bring the w inside as an exponent = lim w -> inf e^ln( (w / (w - 1)) ^ w ) cancel the exponential and log = lim w -> inf (w / (w - 1))^w substitute w = n + 1, so as w -> inf n also -> inf = lim n -> inf ((n + 1)/n))^(n + 1) take out the base of the n+1 exponent to get rid of the 1 = lim n-> inf ((n+1)/n)^n * (n+1)/n write limit of product as product of limits = lim n-> inf ((n + 1)/n)^n * lim n-> inf (n + 1)/n first limit is the normal form of the limit for e, second limit is easily calculated to be 1 = e
@cblpu5575
Жыл бұрын
Recall that the domain of ln (x) is **positive real numbers only** hence x/h is a positive real number x divided by a quantity h tending to zero
😍😍👌👌✊✊👍👍
BRAVO
(1 + 1/(x/h))^(x/h) is not equal e
Always the best teacher.....what about 1/x
@PrimeNewtons
Жыл бұрын
Thanks
He missed step when he used fact that ln is continuous
You are the best
@PrimeNewtons
2 жыл бұрын
Thank you for your kind words.